10. Simple Harmonic Motion and Waves

Calculate the frequency of red light of wavelength 700 nm in a vacuum.

Frequency of red light of wavelength 700 nm: The frequency f of light is given by the formula: f=c/λ Where: c=3×108 m/s (speed of light), λ=700 nm=700×10−9 m Substitute the values: f=3×108/700×10−9=3×108/7×10−7=4.29×1014 Hz Related Questions: A simple pendulum has a time period of 2 s. It is called a second pendulum. Find the length of a second pendulum on … Read more

n a ripple tank of length 1.6 m, waves cover this length in 2 seconds. If the distance between two consecutive troughs is 20 cm, find the number of waves, the frequency of the waves, and their time period.

Waves in a ripple tank: Given: Length of the tank L=1.6 m Time t=2 s Distance between consecutive troughs (wavelength) λ=20 cm=0.2 m The number of waves N can be found as: N=L/λ=1.6/0.2=8 The frequency f is: f=N/t=8/2=4 Hz The time period T is: T=1/f=1/4=0.25 s Related Questions: A simple pendulum has a time period of 2 s. It is called a … Read more

If 10 waves are produced on a long-stretched string of length 1 meter, what is the wavelength of the waves? What will be the frequency of the wave if the speed of the waves is 12 m/s?

Wavelength and frequency of waves: Given: Length of the string L=1 m 10 waves on the string. The wavelength λ is given by: λ=L/number of waves=1/10=0.1 m Given that the speed of the waves is v=12 m/s, we can find the frequency f using the wave speed formula: v=fλ Rearranging for f: f=v/λ f=12/0.1=120 Hz Related Questions: A simple pendulum has a … Read more

What is the time period of a mass-spring system if the mass attached to the spring is 500 g and its spring constant is 20 N/m?

Time period of a mass-spring system: The formula for the time period of a mass-spring system is: T=2π√m/k Where: m=500 g=0.5 kg(convert to kg), k=20 N/m is the spring constant. Substitute the values: T=2π√0.5/20 T=2π√0.025 T≈2π×0.158≈0.993 s Related Questions: A simple pendulum has a time period of 2 s. It is called a second pendulum. Find the length of a … Read more

A pendulum of length 2 m is vibrating on a planet. It completes one vibration in 5 seconds. What is the value of gravitational acceleration on this planet?

3. Gravitational acceleration on a planet: Given: Length of pendulum L=2 m Time period T=5 s. Using the formula for the time period: T=2π√L/g Rearranging for g: g=4π2L/T2 Substitute the given values: g=4π2×2/5 g≈4×9.87×2/25 g≈2.51m/s2 Related Questions: A simple pendulum has a time period of 2 s. It is called a second pendulum. Find the length of … Read more

A simple pendulum has a time period of 5 seconds. What should be the length of the pendulum on the Moon to have the same time period? (Gravitational acceleration on the Moon is of that on Earth.)

Length of the pendulum on the Moon for a 5-second time period: We are given that the time period on the Moon should be 5 seconds. The formula for the time period is: T=2π√L/g Rearrange the formula to find L: L=gT2/4π2L Substitute the values for the Moon: L=1.63×52/4π2 L≈6.53×6.25≈40.8m Related Questions: A simple pendulum … Read more

A simple pendulum has a time period of 2 s. It is called a second pendulum. Find the length of a second pendulum on Earth and on the Moon. (Given: )

Length of a second pendulum on Earth and the Moon: The time period of a simple pendulum is given by the formula: T=2π√L/g Where: T is the time period, L is the length of the pendulum, g is the acceleration due to gravity. We are given that T=2s for a second pendulum. On Earth: Acceleration … Read more

What is the significance of wave speed in a medium?

Wave speed determines how quickly a wave propagates through a medium. It depends on the medium’s properties, such as density and elasticity, and is calculated using v = fλ . Related Questions: Give an example of vibratory motion which is not simple harmonic motion. Give a reason for your selection. At the extreme position, velocity … Read more

How does damping affect oscillatory motion?

Damping is the gradual decrease in amplitude due to resistive forces like air resistance or friction. It reduces energy in the system, eventually stopping the oscillations. Related Questions: Give an example of vibratory motion which is not simple harmonic motion. Give a reason for your selection. At the extreme position, velocity is zero but acceleration … Read more

Why does a simple pendulum have a longer time period on the Moon than on Earth?

The time period of a pendulum depends on gravity . Since the Moon’s gravity is weaker than Earth’s, the time period T=2π√L/g g increases, making the pendulum oscillate more slowly. Related Questions: Give an example of vibratory motion which is not simple harmonic motion. Give a reason for your selection. At the extreme position, velocity … Read more